The present study was motivated by the theory-method mismatch between heterotypic continuity (aspects of development that manifest differently across the lifespan thus cannot be measured the same way over time) and longitudinal measurement equivalence (the statistical assumption that the developmental phenomenon studied is measured on the same metric with equal precision across time). To investigate under which conditions measurement non-equivalence might pose threats to the validity of research conclusions from latent growth curve models, this dissertation investigated: (1) Under which conditions violations of longitudinal measurement equivalence impacted the accuracy (bias and stability) of the growth parameters, (2) How well model fit measures (model chi-square, RMSEA, CFI, and TLI) and the likelihood ratio test performed under varied magnitudes, locations, and percentages of non-equivalence, and (3) How stability and bias of the growth parameters and performance of fit measures compared in linear growth, quadratic growth, and latent basis curve models. To examine the performance of the first-order latent growth curve model when longitudinal measurement equivalence was violated, data were generated resembling children's nonlinear growth, with systematically varied magnitudes of non-equivalence (high; medium; low), locations of non-equivalence (item difficulty parameters; item discrimination parameters; both), and percentages of items impacted. Data were generated under a longitudinal IRT 2-PL model with four measurement occasions, then collapsed into composite variables (means). Measurement non-equivalence progressively increased starting with the second measurement occasion. Sample size and number of items were varied to represent conditions in the child development literature. A pattern emerged when examining bias, stability, and fit measure performance for all three models. The outcome variables were hardly influenced by measurement equivalence violations in the item discrimination parameter yet shifted systematically in response to violations involving the item difficulty parameter. Additionally, the quadratic model often fit unreasonably well; fit was similar regardless of the severity of non-equivalence, especially for CFI and TLI. Results suggest that the latent growth curve model is not robust to longitudinal measurement non-equivalence, and that the type and amount of damage varies with proprieties of the violation itself. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]